Water balloons of different masses are launched by slingshots at different launching velocities v. All have the same vertical component of launching velocities.
a. Rank by the time in the air, from longest to shortest.
b. Rank by the maximum height reached, from highest to lowest.
c. Rank by the maximum range, from greatest to least.
(a)
To rank: The balloons on the basis of time in the air, from longest to shortest.
Answer to Problem 16A
The rank of balloons is,
Explanation of Solution
Given:
Water balloons of different masses are launched by slingshots at different launching velocities as shown below.
Formula used:
Horizontal component of initial velocity of projectile is,
Vertical component of initial velocity of projectile is
Where,
u is the initial velocity.
Time of flight is the amount of time required for projectile to complete its trajectory,
Calculation:
Consider case ( A )
Vertical component of velocity is,
Time of flight is
Consider case ( B )
Vertical component of velocity is,
Time of flight is
Consider case ( C )
Vertical component of velocity is,
Time of flight is
Consider case ( D )
Vertical component of velocity is,
Time of flight is
Conclusion:
Therefore, time in the air, from longest to shortest is,
(b)
To rank: The balloons on the basis of maximum height reached, from highest to lowest.
Answer to Problem 16A
The rank of balloons is,
Explanation of Solution
Given:
Water balloons of different masses are launched by slingshots at different launching velocities as shown below.
Formula used:
Calculation:
Consider case ( A )
Maximum height is,
Consider case ( B )
Consider case ( C )
Consider case ( D )
Conclusion:
Maximum height reached, from highest to lowest is,
(c)
To rank: The balloons on the basis of maximum range, from greatest to least.
Answer to Problem 16A
Maximum range, from greatest to least is,
Explanation of Solution
Given:
Water balloons of different masses are launched by slingshots at different launching velocities as shown below.
Formula used:
Range of projectile is,
Calculation:
Consider case ( A )
Range of projectile is,
Consider case ( B )
Range of projectile is
Consider case ( C )
Range of projectile is,
Consider case ( D )
Range of projectile is,
Conclusion:
Therefore, maximum range, from greatest to least is,
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Conceptual Physics: The High School Physics Program
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